Out of 5 women and 4 men a committee of three members is to be formed in such a way that at least one member is a woman. In how many different ways can it be done?

Explanation:

The committee will be formed as follows:

(i) 1 woman and 2 men

(ii) 2 women and 1 man

(iii) 3 women

Therefore, Required number of committees

=5C1×4C2+5C2×4C1+5C3

= 5× 4×3\1×2 + 5×4\1×2 × 4 + 5×4×3\1×2×3

= 30 + 40 + 10 = 80